I have the Sigma lens on my Nikon D50 and although I don’t have the Tamron 70-300, I do have the 28-300 which regularly gets slated for being soft and yet I get consistently good results from it. I’ve never really found a significant difference in any ‘budget’ lenses and with glass you really do get what you pay for. That said, lenses each have their own little traits. My basic Canon 75-300 is a little sharper than my Tamron 28-300 but suffers much more chromatic abberation. My Sigma 50-500 has tremendous range and flexibility but isn’t as sharp as my Canon 70-200L, which optically is absolutely stunning and mindblowingly sharp but sometimes I miss having the extra range.
In all honesty, the thing that will dictate how your images look is how good your shooting technique and editing skills are, not whether you decide to go for the Tamron or the Sigma. Both lenses are more than capable of giving good results of handled well.
Paul